Construction of Boolean contact algebras

Abstract

We consider Boolean algebras endowed with a contact relation which are abstractions of Boolean algebras of regular closed sets together with Whitehead's connection relation [17], in which two non‐empty regular closed sets are connected if they have a non‐empty intersection. These are standard examples for structures used in qualitative reasoning, mereotopology, and proximity theory. We exhibit various methods how such algebras can be constructed and give several non‐standard examples, the most striking one being a countable model of the Region Connection Calculus in which every proper region has infinitely many holes.